A self-consistent model of electron emission from metals

We present a model of electron emission from metals, which takes into accou nt deviation of the electron distribution function from the Fermi equilibri um form inside the cathode under the emission effect. Using the Grad method electron distribution function, the emission boundary is expressed consecu tively in terms of its hydrodynamic moments: temperature, average velocity, heat nux density. These hydrodynamic moments are caused by the emission it self and thus need a self-consistent determination. New easy-to-use equatio ns for the emission current density, emission heat flux, total energy distr ibution function of the emitted electrons are proposed. Consideration was m ade for a wide range of temperatures (less than or equal to 3500 K), field strengths (less than or equal to 1.5x10(8) V/cm) and work function (3.0 to 4.5 eV) of the emitter. A considerable deviation from the Fowler-Nordheim ( FN) theory was found at high current density (>10(9) A/cm(2)).